random angle ? ∈ [0, 360) (in degrees) and a random radius ? ∈ [0, 1] (in meters) both independent and uniform. Calculate the density of the variables ? and ? (the cartesi

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Consider that a ball is thrown with a random angle ? ∈ [0, 360) (in degrees) and a random
radius ? ∈ [0, 1] (in meters) both independent and uniform. Calculate the density of the
variables ? and ? (the cartesian coordinates of the point at angle ? and radius ?) as well as their
expectation and variance.

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I would like to know why the integral of 1/sqrt(1+t2) is considered arctan(t). This is not the case as per the rules of integration.

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